A 25 kg box is dragged across a floor by a rope that makes an angle of 60 degrees with the horizontal. The tension in the rope is 100 N while the box is dragged 15 m.
A) how much work is done by tension?
B) how much work is done by gravity?
horizontal rope force= 100 cos 60
= 50 N
so
a) work done by tension = 50*15
= 750 Joules
b) NONE !!!! there is no vertical displacement !
To find the work done by tension and gravity, we need to use the formulas:
Work = Force * Distance * cos(theta)
where:
- Work is the work done by the force (in joules, J)
- Force is the magnitude of the force applied (in newtons, N)
- Distance is the distance over which the force is applied (in meters, m)
- theta is the angle between the force applied and the direction of motion (in degrees)
Given:
- Mass of the box (m): 25 kg
- Angle between the rope and the horizontal (theta): 60 degrees
- Tension in the rope: 100 N
- Distance the box is dragged: 15 m
A) To find the work done by tension, substitute the values into the formula:
Work by tension = Tension * Distance * cos(theta)
Work by tension = 100 N * 15 m * cos(60 degrees)
Work by tension = 100 N * 15 m * 0.5
Work by tension = 750 J
So, the work done by tension is 750 joules (J).
B) To find the work done by gravity, we need to determine the gravitational force acting on the box. The weight or gravitational force (Fg) is given by:
Weight (Fg) = mass * acceleration due to gravity
Weight (Fg) = 25 kg * 9.8 m/s^2
Weight (Fg) = 245 N
Now, substitute the values into the formula:
Work by gravity = Weight * Distance * cos(theta)
Work by gravity = 245 N * 15 m * cos(60 degrees)
Work by gravity = 245 N * 15 m * 0.5
Work by gravity = 1837.5 J
So, the work done by gravity is 1837.5 joules (J).
To find the work done by tension and gravity, we need to use the formulas:
Work = Force × Distance × cos(θ)
where:
- Work is the amount of work done
- Force is the magnitude of the force being applied
- Distance is the distance over which the force is being applied
- θ is the angle between the direction of the force and the direction of the displacement
For Part A, to find the work done by tension:
- Force = 100 N (given)
- Distance = 15 m (given)
- θ = 60 degrees (given)
Plugging these values into the formula, we have:
Work = 100 N × 15 m × cos(60°)
To calculate cos(60°), we can use a scientific calculator or reference table, which gives us the value of cos(60°) as 0.5.
Therefore, the work done by tension is:
Work = 100 N × 15 m × 0.5
Work = 750 Joules
So, the work done by tension is 750 Joules.
For Part B, to find the work done by gravity:
Gravity does work on an object when it acts in the same direction as the displacement. Since the box is being dragged horizontally, the force of gravity does not act in the same direction as the displacement. Therefore, the work done by gravity is zero.
Hence, the work done by gravity is zero Joules.